{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YVCC5MPQYK5U6YVC4YVIM3ISCA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2ed375e2b8ae062a4c203e1bb0be64f6e4b1818efdaced9e2d036990c6c9b63a","cross_cats_sorted":["math.GR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-16T21:18:42Z","title_canon_sha256":"4341d0e32bbe390cbe7ce256ff2e72157a6a8acd8a0997941d9156d4958c5b64"},"schema_version":"1.0","source":{"id":"1305.3937","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3937","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3937v2","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3937","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"YVCC5MPQYK5U","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YVCC5MPQYK5U6YVC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YVCC5MPQ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:d7b23e7512a684aeebab92f05cf7a23a6b3d8731c9246f16ccbaca1f2c518853","target":"graph","created_at":"2026-05-17T23:44:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study $C_{a, b}$ curves and their applications to coding theory. Recently, Joyner and Ksir have suggested a decoding algorithm based on the automorphisms of the code. We show how $C_{a, b}$ curves can be used to construct MDS codes and focus on some $C_{a, b}$ curves with extra automorphisms, namely $y^3=x^4+1, y^3=x^4-x, y^3-y=x^4$. The automorphism groups of such codes are determined in most characteristics.","authors_text":"Q. Wang, T. Shaska","cross_cats":["math.GR","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-16T21:18:42Z","title":"On the automorphism groups of some AG-codes based on $C_{a, b}$ curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3937","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0db1fd4280507c00c9dddbd2c9681aebde6a886ff55da006ae0c5ccc8b13e299","target":"record","created_at":"2026-05-17T23:44:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2ed375e2b8ae062a4c203e1bb0be64f6e4b1818efdaced9e2d036990c6c9b63a","cross_cats_sorted":["math.GR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-16T21:18:42Z","title_canon_sha256":"4341d0e32bbe390cbe7ce256ff2e72157a6a8acd8a0997941d9156d4958c5b64"},"schema_version":"1.0","source":{"id":"1305.3937","kind":"arxiv","version":2}},"canonical_sha256":"c5442eb1f0c2bb4f62a2e62a866d121014381a8bc382d256f5c6506d08509470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5442eb1f0c2bb4f62a2e62a866d121014381a8bc382d256f5c6506d08509470","first_computed_at":"2026-05-17T23:44:48.764915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:48.764915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O0DlLjivr8n6Z3LL5VmS+XwVCZFSL6JLc4AoAd3IJRmbRMVG/1I2IsO1CsjRpVf2bXED81bEnLgIXQMdqZmxAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:48.765530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3937","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db1fd4280507c00c9dddbd2c9681aebde6a886ff55da006ae0c5ccc8b13e299","sha256:d7b23e7512a684aeebab92f05cf7a23a6b3d8731c9246f16ccbaca1f2c518853"],"state_sha256":"e52319cbc08acf77775fa23a221d3a2dd03c4ec5f6891e2aba90775ec240856d"}